In 1938, his second year in the game, Jesse was with the major league Chicago White Sox from April 26 to May 11, a run of 16 days, appearing in four games with no hits in six at-bats and spent the rest of his sixteen-year career in the minor leagues.

During his minor league career, Jesse appeared with sixteen different
teams in ten different leagues, playing in both the infield and outfield. He would hit over the .300 mark in six of his seasons, with his biggest numbers (not adjusted for league) coming in 1948 when he hit over the coveted .400 figure with a .411 average and slugged at a .650 clip, with seventeen home runs, while serving as player-manager for the Bryan Bombers of the class C Lone Star League.

One would think, however, that he played to his best in 1944 while with the Kansas City Blues, of the class AA (then the highest tier of the minors) American Association, hitting .311 with ten home runs in 562 at-bats. You could also say that his rookie season in 1937, when he hit .348 with five homers, for the St. Paul Saints of the same AA league was an even match. Landrum would finish his active time in 1953 at the age of forty and his minor league numbers show that he appeared in 1,521 games with a .304 batting average that includes 95 home runs. Jesse finished his last years in the minor leagues (1947-1953) as a player-manager for six different teams.